For example, if I say the name “Mary Jane”, the 2nd part (Jane) is stronger, but if I add her surname, then the stress moves to the last name “Mary Jane Smith”. This is also true for place names, for example, “New York” is stressed on the second part, but “New York City” is stressed on the the 3rd part.

Exceptions
Names which use the words “street” or “store” actually use regular compound noun stress, which means that the first part is stronger: Sixth Street / Oak Street / Jackson Street / Wall Street / General Store / Target Stores.

Be on the lookout for compound nouns, you are likely to find them any time you hear or read something in English! (These are the ones I used to write this blog post: stress pattern / last name / place names / lookout / blog post.)